If, \frac{x^2+ 1 -2 x}{x^2+1+2x }=4/5, then what is the value of x+ 1/ x ?

SSC CPO SI and ASI Model Paper 1

Question : 138 of 200

Marks: +1, -0

If, ${x^2+ 1 -2 x}/{x^2+1+2x }=4/5$ , then what is the value of $x+ 1/ x$ ?

Solution:

{x^2 +1–2x} /{x ^2+1+2x }=4/5

{x[ x + 1/x – 2]}/x [x + 1 /x+ 2 ]=4/5

Let

x + 1 /x=y

∴(y - 2) /(y+ 2 )=4/5

⇒5y – 10 = 4y + 8⇒ y = 18

∴x + 1/x= 18

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